Day 130 #teach180 Inverse of a Function

March #MTBoSBlog18

A few highlights from the past weeks…

Wear Red 

Public Education Week!  Politics can be emotionally draining.  All I want to do is focus on my students, but our elected governor in Kentucky has been pretty harsh toward public education in recent weeks.  In my opinion, it has been bullying at its worst.  But I am proud of the work so many are doing to make the issues known.  It is our duty to contact our legislators and let them know how this will affect us and our communities.  I am very proud to be a public education teacher!!!

Box Designer

Last week in my class that uses Springboard – we were looking at a different linear model.  It followed the direct variation lesson a couple of days later.  I’m not sure I really caught on to this lesson’s BIG ideas last year or even last semester, but this semester – I had a couple of a-ha moments!

I’ve been stacking cups since at least 2002.  You can read about different experiences here (9 things) and here (Attend to Precision).

What I love about SB lessons is the minute details that I miss when I go through during my planning time – but that pop up when I’m observing the groups working.  This particular lesson had students collect data on heights on stacks of two different cups.

As they graphed the data of one style of cup.  It asked them to describe anything they noticed in the data / graph.  Then they were asked to write a linear model of their data.  So many simply wrote the equation h = 1.5 n, h height and n number of cups with their cup’s rate of change…  so as I used a ruler and “graphed” their equation, they saw they needed to adjust to translate the line up… or else the model would under predict the stack’s height.

On the following page, students were then asked to graph the line of their equation model.  Then how the two graphs were alike / different?  Such a simple little move – yet – it focused students in to discrete data – a finite set, continuous from the model – continuing even beyond the coordinate plan shown.

They discussed how the data did not actually have a y-intercept since it would not make sense to have 0 cups with a height – but they realized the y-intercept of the equation corresponded to the hidden part of the cup without the lip and even how their model needed the y-intercept, otherwise it would not accurately predict the heights.

A question about domain and range – was useful to compare how we might define a reasonable domain for the data and the equation.

As students continued, they were asked to define the base of their box using a square.  It was quite interesting to listen in as some suggested a base with side measure equal to the actual cup diameter.  Some quick a-ha’s from their discussions were heard.

As we wrapped up the lesson, one student in particular said to me – I like doing things like this.  When we do normal math, I kind of get lost and bored with all the steps, but this interests me and I’m able to reason out my answers and make connections to the math.  My reply… “this is real math”  the other is the “fake math.”

Green Pens!

I FINALLY got my green pens out.  I found that doing a quick retrieval quiz at the beginning of class from either the previous day’s work or from a couple of days earlier is a great place for these.  I kept my supply of green pens in my pocket and walked the room – observing.  I would eventually find 4 or 5 students who had the correct work / solutions and I handed them the pens and asked them to check / verify their classmates work.

What I liked – it gave them something to do for the 3 or so minutes others were finishing up.  I liked getting a variety of students to help.  Although I did not get to view every single student’s approach / work, this gives me the opportunity to visit students who have been absent and/or I expect to struggle and have one-on-one time with them.  A few even surprise me, stepping up and getting done more efficiently because they want to check others with the green pen!

I need to get some color dry erase markers to use when we are retrieval practicing on the white boards!